What is the integral of (5+9x)^8(9) ?

The integral of (5+9x)^8(9) is 1/9 (5+9x)^9+C

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integral of (5+9x)^8(9)

\int (5 + 9 x)^{8} (9) d x

\frac{1}{9} (5 + 9 x)^{9} + C

Solution steps

\int (5 + 9 x)^{8} \cdot 9 d x

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= 9 \cdot \int (5 + 9 x)^{8} d x

Apply u-substitution

: \int \frac{u ^{8}}{9} d u

= 9 \cdot \int \frac{u ^{8}}{9} d u

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= 9 \cdot \frac{1}{9} \cdot \int u^{8} d u

Apply the Power Rule

: \frac{u ^{9}}{9}

= 9 \cdot \frac{1}{9} \cdot \frac{u ^{9}}{9}

Substitute back

u = 5 + 9 x

= 9 \cdot \frac{1}{9} \cdot \frac{( 5 + 9 x ) ^{9}}{9}

Simplify

9 \cdot \frac{1}{9} \cdot \frac{( 5 + 9 x ) ^{9}}{9} : \frac{1}{9} (5 + 9 x)^{9}

= \frac{1}{9} (5 + 9 x)^{9}

Add a constant to the solution

= \frac{1}{9} (5 + 9 x)^{9} + C

\int \frac{cos ^{3} ( x )}{sin ( x )} d x

\int \frac{2 x + 4}{x ^{2} + 5 x - 6} d x

y = x^{3} - 7 x, y = - 4 x + 2

x \to 2 lim ((x + 4)^{2})

\frac{6 + sin ( x )}{6 x + cos ( x )}

What is the integral of (5+9x)^8(9) ?
The integral of (5+9x)^8(9) is 1/9 (5+9x)^9+C